Abstract
In this paper, the nodal structure for simple atomic systems is revisited and a procedure for identifying the symmetry properties and nodal structure of the time and spin independent Schrodinger equation will be presented. Application is made to the few electron atom, and explicit new nodal surface equations are given for states of various symmetries. In the construction of trial functions for variational calculations in quantum mechanics and in the choice of nodal surfaces needed in Monte Carlo calculations to obtain fermion solutions to Schrodinger’s equation for spin independent Hamiltonians, the accuracy of the calculations can be strongly influenced by the initial choice of the trial functions. We incorporated these newly found nodal conditions in the trial functions, and energy eigenvalues were calculated with better accuracy for different symmetries.
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